I would much rather reload a shotgun, under stress or time constraints, than a lever rifle, through its tiny loading gate. (Not all lever rifles use a tube magazine, and a loading gate, on the side, but the OP specified .357, so, unless I am forgetting something, that means using a rifle that loads through a side-mounted loading gate.)
If I have to shove individual cartridges through a loading gate, I would rather that they be larger than .38 Special or .357 Magnum. I briefly owned two Marlin .357 1894 lever rifles, that I purchased with OT money earned after Hurricane Ike, when we were still interested in starting CAS, but never learned to like them. I think one of them may have been yet unfired when I sold or traded both of them, perhaps in one transaction.
Having not liked shoving tiny .38/.357 cartridges into a loading gate, I replaced the Marlins with a Miroku-made Winchester 1892, in .45 Colt, which was easier to load, but it was an unreliable feeder, so not a candidate for defense. We never got around to joining CAS, so this Mirokuchester was sold or traded, some years ago.
We recently acquired his-and-hers Winchester ‘94 AE Trappers, .45 Colt, pre-owned, from a local gun store. We have yet to try tem in live-fire. The COVID situation has prevented us from getting out to a range with them.
Over time, Rossi clones of the Winchester 1892 have not earned the best reputation. My wife’s Rossi jammed hard, when being fed .38 Specials, and I thought I would never manage to get it cleared. After the jam was was cleared, each cartridge, as it left the mag tube, was trying to feed at a too-steep angle. I realize that some folks love their Rossis, but I have a negative opinion.
I would much rather use a box-magazine-fed lever rifle, such as a Browning BLR, if I had to use a lever rifle for defensive purposes. These fire true rifle cartridges, so have to be used on a range that accommodates such ammo.
From what I have seen of Cowboy Action Shooting, it is not very practical/tactical. When we were interested in trying CAS, there was a local LEO who had a hand in running local matches, who injected some level of practical/tactical into the game, but when he promoted to LT, his schedule changed, hindering his continued participation. Our interest declined, before we had accumulated all the necessary firearms.
Really, my wife is the one who drives the interest in lever-rifling, with traditional side-loading-gate lever rifles, in our household. I have two Browning BLRs, one a Takedown, which I like, but I have yet to warm-up to traditional lever rifles.